Original battery was dying; only 3 minutes of power remaining even after full charge.
It went well! And the video guide was great. Got it done all within 15 minutes with the right tools. I'm happy. So's my wife; it's her MBP :)
Nothing more to add, really. I suppose I could add this advice: do remember to clean out the dust accumulated inside, especially around the cooling fan. Just some light dusting will do. That's all.